\documentclass[]{article}

\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{caption}
\usepackage{float}
\usepackage{xfrac}
\usepackage{marvosym}
\usepackage{ltxcmds} % get commands: \ltx@empty, \ltx@carzero
\usepackage{enumerate}
\usepackage{array}
%\usepackage[sort&compress]{natbib}

%\usepackage{hyperref}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{textcomp}
\usepackage{amsthm}
\usepackage{bigstrut}
\usepackage[margin=1in]{geometry}
\usepackage{natbib}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{color}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{cancel}
\usepackage{chngcntr}
\usepackage{extarrows}
\usepackage{epstopdf}  
\usepackage{bigstrut} 
\usepackage{rotating} 
\usepackage{multirow} 
\usepackage{booktabs} 
\usepackage{authblk}
\usepackage{bbm}

%dfdfd
\usepackage{epstopdf}
\epstopdfsetup{update}
\usepackage{epsfig}
\usepackage{booktabs}
\usepackage{pgf}
\usepackage{float}
\usepackage{subfig}
\usepackage{ifthen}
\usepackage{multirow}
%dfdfd



\theoremstyle{definition}% default plain
\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
\newtheorem{cor}{Corollary}
\renewcommand{\qedsymbol}{$\blacksquare$}
\newtheorem{lem}{Lemma}
\newtheorem*{notation}{Notation}


\theoremstyle{definition}
\newtheorem*{defn}{Definition}
\newtheorem{conj}{Conjecture}
\newtheorem{exmp}{Example}
\newtheorem{ass}{Assumption}
\newtheorem{prope}{Property}
\newtheorem{note}{Note}
\newtheorem{remark}{Remark}
\newtheorem{obs}{Observation}
\newcommand{\Gbar}{\overline{G}}
\newcommand{\Hbar}{\overline{H}}
\newcommand{\Fbar}{\overline{F}}
\newcommand{\Ex}{\mathbf{\mathbb{E\/}}}
\newcommand{\ind}[1]{\mathbbm{1} (#1)}

\newcommand{\pEx}[2]{\mathbf{E\/}\big(#1,#2\big)}
%\newcommand{\hr}[2] {
%\dfrac{#1(#2)}{\overline{\MakeUppercase#1}(#2)}}
%\newcommand{\hrt}[1] {
%\dfrac{#1(t)}{\overline{\MakeUppercase#1}(t)}}
%\newcommand{\Pr}{\mathbb{P\/}}
\newcommand{\diff}[2] {
\frac{d}{d #2}#1}
\newcommand{\hrate}[2] {
\mathbf{r}_{#1}(#2)}
\newcommand{\surv}[2]{\mathbf{\overline{F}}_{#1}(#2)}
\newcommand{\cdf}[1]{\mathbf{\overline{F}}_{#1}}
\newcommand{\pdf}[2]{\mathbf{{f}}_{#1}(#2)}
\newcommand{\MG}[2]{\mathbf{{MG}}_{#1}(#2)}
%\counterwithin{cor}{thm}
%\counterwithin{cor}{lem}
\newcommand{\noat}[1]{\textcolor{red}{ #1}}
\newcommand{\pr}{\mathbb{P}\/}
\newcommand{\prr}[1]{\mathbb{P} \big[ #1\big]  }
\newcommand{\ve}[1] {\mathbf{#1}}
\newcommand{\RR}{\mathbb{R}}


\makeatletter
\newtheorem*{rep@theorem}{\rep@title}
\newcommand{\newreptheorem}[2]{%
\newenvironment{rep#1}[1]{%
 \def\rep@title{#2 \ref{##1}}%
 \begin{rep@theorem}}%
 {\end{rep@theorem}}}
\makeatother


\newtheorem{theorem}{Theorem}
\newreptheorem{theorem}{Theorem}
\newtheorem{corollary}{Corollary}
\newreptheorem{corollary}{Corollary}